A "brief" history of the Sport.
How Parachutes have evolved into Paragliders & beyond

1100's - The  chinese amused themselves by jumping from  high places with rigid umbrella like structures. They also used kites used for dropping bombs on their enemies.

1495 - Leonardo Da Vinchi designed a pyramid shaped parachute, held open by 4 wooden poles.

1595 - Fausto Veranzio jumped from a tower in Venice with a wooden & canvas rig.

1687 - In Siam a court jester would jump from high places with two large umbrella's. The wind carried him onto rooftops, trees & into the nearby river.

1783 - Sebastian Lenormand jumped from a tower with a 14 foot diameter parachute.

1785 - The collapsible silk parachute was designed by JP Blanchard. He jumped from a balloon & broke a leg.

1797 - Andre Garnerin made many jumps, one from 8,000 feet over London.

1800's several more jumps were made with several designs, including an inverted cone.

1887 - the first parachute harness was designed.

1903 - Wright Brothers first powered flight.

1911 - Pilot Chute invented - to drag a parachute out of its container. The first freefall was made.

1913 - First soaring type parachute was designed. World War 1 cancelled further plans!

1914 - After Tiny Broadwich's static line getting caught up in the aircraft, on her next jump she cut the line & pulled it her self - the first manually operated parachute.

1929 - A triangular canopy was patented.

1930 - The Russians held the first accuracy contests.

1932 - The Americans had a try at accuracy.

1941 - The Germans dropped 14,000 paratroopers onto Crete.

1948 - FAI formed

1948 - Dr Francis Rogallo & NASA developed the flexible delta kite.

1954 - Fred Mason patented a "T" cut in round canopies giving forward drive.

1960 -  Capt Joseph  Kittinger fell from his balloon at 102,000 feet, reaching 702 mph in freefall.

1961 - Tom Purcell Jr was tow launched on a Rogello Kite in USA.

1961 - Ascending Parachutes were thought up, & towed Parascending began.

1962 - The Paracommander was developed. A steerable parachute with holes EVERYWHERE!
Paracommander Mark 1

1962 - John Dickinson flew a Rogallo wing.

Late 60's Parawing based on Rogallo's design.

1964 - The First Square Ram Air Para Foil was invented by Domina Jalbert in Florida.

1968 - The Para Wing was developed in America by Steve Snyder. Para-Plane  Para-Foil

1968 - Parachutes were foot launched from the shores of lake placid. Article appeared in Parachutist magazine.

1969 - The Para Plane was developed by Steve Snyder. (See Above)

1970 - The Ram Air Canopy became the industry standard.

1973 - The British Association of Paragliding Clubs was formed, after the British Parachute Association withdrew support.

1970's - The Sport of Hang gliding became increasingly popular.

1980's - In French & Swiss Alps a small number of parachutists began launching from steep slopes to emulate hang gliders.

1980's - "In the United Kingdom there was Gerald Williams, a lone hang glider pilot who could be seen drifting to earth beneath his canopy in the Peak District whilst his fellows shook their heads & muttered that it would never catch on...." :-)

Jump canopy paraglider  Early 90's paraglider

1980's -1990's Paragliding canopy design was developed from jump parachutes - to provide optimum glide.
The design was refined to have high lift aerofoils, narrower cell entries & long slender wings.
Speed bars that pull down on front risers & give even more drive were developed.

1992 The British Hang Gliding Association & British Association of Paragliding Clubs amalgamated to form the British Hang Gliding & Paragliding Association.

Paramotoring.
Similar to paragliding, only with a big fan strapped to ones back.

Paraskiing.
With a pair of Skis strapped to your feet, off you go, down the slope & fly. "The Ski Launch"

Power Kiting
A big ram air kite with long strings - not powerful for sustained flight but lengthy "hops" can be achieved, as well as incredible groundspeed. Sometimes used in conjunction with a 4 wheel or 3 wheel buggy

Kite Surfing
Similar to power kiting only with a surf board & done at sea!

Latest Developments:

2001 - Someone in France is Skydiving with a wingsuit for longer freefall with a modified paragliding canopy for a longer canopy ride.

2002 - Someone is BASE jumping a paragliding canopy. Suspending the canopy over the side of  a bridge - & then jumping OVER it. Having a canopy & its lines BELOW you is not reccomended.
 
Reference material.
1) Parachuting, The Skydivers Handbook. Dan Poyner & Mike Turoff
2) Touching Cloudbase 3rd Edition.  Ian Currer & Rob Cruishank.